messages listlengths 1 1 | ground_truth stringclasses 13
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, m: 3}. What is the expected number of occurrences of the pattern 't.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, b: 1, m: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {y: 1, z: 1, k: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, i: 3}, what is the expected number of times the pattern 'i+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, d: 3}. What is the expected number of occurrences of the pattern 'sd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, d: 1, r: 1, m: 1}. What is the expected number of occurrences of the pattern 'mr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 3, i: 1}, what is the expected number of times the pattern 'h+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, r: 2}, what is the expected number of times the pattern 'r.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, e: 3}. What is the expected number of occurrences of the pattern 'e+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, i: 2, s: 1}. What is the expected number of occurrences of the pattern 'i.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {f: 1, d: 1, o: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, n: 1, r: 1, s: 1}. What is the expected number of occurrences of the pattern 'n+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 3, t: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 3, t: 1}, what is the expected number of times the pattern 'ht+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, y: 1, r: 2}, what is the expected number of times the pattern 'v*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, c: 1, f: 1, w: 1}. What is the expected number of occurrences of the pattern 'c.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, z: 1, o: 1, m: 1}, what is the expected number of times the pattern 'z*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, o: 1, d: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, k: 1, o: 1, s: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, b: 1, y: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 1, p: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'pi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 2, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, u: 1, e: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'ul+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, x: 2}, what is the expected number of times the pattern 'x*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, l: 1, x: 1, w: 1}. What is the expected number of occurrences of the pattern 'wx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, p: 1, j: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, r: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 3, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, t: 3}. What is the expected number of occurrences of the pattern 'y.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, x: 2}, what is the expected number of times the pattern 'xq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, s: 3}, what is the expected number of times the pattern 'sy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 3, y: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, d: 2, v: 1}. What is the expected number of occurrences of the pattern 'd.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {g: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'a+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, j: 1, s: 1, m: 1}, what is the expected number of times the pattern 'je*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'tb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, e: 1, i: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, u: 1, d: 1, v: 1}. What is the expected number of occurrences of the pattern 'v*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, y: 1, w: 1, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 2, j: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {g: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {a: 3, p: 1}. What is the expected number of occurrences of the pattern 'ap*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {u: 2, m: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'un+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, j: 1, q: 2}. What is the expected number of occurrences of the pattern 'l+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {t: 1, i: 3} to form a word, what is the expected number of matches of the pattern 't*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'pf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, p: 1, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, k: 1, o: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 1, e: 1, m: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'mc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, z: 1, x: 1, h: 1}, what is the expected number of times the pattern 'nz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {a: 1, x: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, k: 1, y: 1}. What is the expected number of occurrences of the pattern 'my+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, e: 2, r: 1}. What is the expected number of occurrences of the pattern 'fr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, t: 2}. What is the expected number of occurrences of the pattern 't.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 2, o: 1, p: 1}. What is the expected number of occurrences of the pattern 'rp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 2, g: 2}, what is the expected number of times the pattern 'g*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, t: 3}. What is the expected number of occurrences of the pattern 'tp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 2, a: 2}, what is the expected number of times the pattern 'at*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, i: 3}, what is the expected number of times the pattern 'y+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 3, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 2, y: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'uy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 2, f: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, b: 3}, what is the expected number of times the pattern 's*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, n: 1, y: 1, k: 1}. What is the expected number of occurrences of the pattern 'ny+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {z: 2, x: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, u: 3}, what is the expected number of times the pattern 'ui+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {h: 3, m: 1}. What is the expected number of occurrences of the pattern 'm*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, o: 1, q: 2}, what is the expected number of times the pattern 'f.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 1, q: 1, w: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'w*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, o: 1, x: 1, j: 1}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 2, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {u: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {w: 1, b: 1, p: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {c: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'c*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 2, x: 1, k: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {z: 2, k: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, d: 2}. What is the expected number of occurrences of the pattern 'dx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, z: 1, d: 1}. What is the expected number of occurrences of the pattern 'z*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {t: 3, i: 1}. What is the expected number of occurrences of the pattern 'it*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, m: 1, t: 1}. What is the expected number of occurrences of the pattern 'dm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {m: 2, r: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'vd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 1, b: 1, v: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'ip*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, j: 1, h: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, n: 2}, what is the expected number of times the pattern 'n*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {z: 2, v: 1, t: 1}. What is the expected number of occurrences of the pattern 'v.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'd+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 3, x: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, m: 1, y: 2}. What is the expected number of occurrences of the pattern 'm*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, w: 1, s: 2}. What is the expected number of occurrences of the pattern 'w*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {c: 1, a: 1, r: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'a*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
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